Influence of the surface curvature of carbon nanotubes on their conductivity in the dirac approximation

A method of surface curvature of carbon nanotubes has been proposed for quantitative estimation of the longitudinal conductivity of nanotubes. A dispersion relation for the electron spectrum of single-walled carbon nanotubes has been obtained analytically. The change in the zone structure of nanotubes of various types and diameters caused by taking into account the surface curvature has been analyzed. The temperature dependence of the longitudinal component of conductivity with allowance for the surface curvature for a series of nanotubes has been calculated. The comparison with the conductivity of a plane graphene has been performed. It has been shown that, in zig-zag tubes, the correction of the conductivity for the surface curvature decreases with an increase in temperature as well as with an increase in the radius of curvature.